Probability: "In Prime High School, there are 3 language classes - Italian, German and French...."

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Stardust1

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Hey guys, can you please help me solve this problem:
In Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
Thanks
 
Stardust1 said:
Hey guys, can you please help me solve this problem:
In Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
Thanks
Click to expand...
What are your thoughts? What have you tried? How far have you gotten?

Please re-read the "Read Before Posting" message, and reply with the requested information, starting with what topic in your statistics class generated this exercise.

Thank you!
 
Stardust1 said:
Hey guys, can you please help me solve this problem:
In Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
Thanks
Click to expand...
I don't think there's enough information (even after realizing that the 40 is not the total of all students, but the number in each of 3 classes). Please check that you copied the entire problem.

I tried filling out a Venn diagram. putting x in the region for "only Italian", and putting expressions in other unknown regions. I find that there is no equation I can solve for x, so we need one additional fact. (I could just be missing something ...)
 
Dr.Peterson said:
I don't think there's enough information.... Please check that you copied the entire problem.

I find that there is no equation I can solve for x, so we need one additional fact...
Click to expand...
Stardust1 said:
In Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
Click to expand...
I suspect that the "and" in "German and Italian" is meant to be an "or". If so, then the exercise solves nicely.
 
Dr.Peterson said:
Do you mean 12 study only German or Italian [or both], or perhaps 12 study only German or only Italian, or something else? I don't see it working out.
Click to expand...
Glad you asked because I assumed that the meaning of @stapel's statement was obvious to native speakers.:)
 
I'm not sure if the OP's first language is English so what follows might not be true for this poster.

It amazes me how students, whose 1st language is English, do not know the difference between and/or and greater than/less than.
 
The poster's IP address resolves to Australia. But Australia has a very high proportion of immigrants.
 
blamocur said:
Why the title of the thread starts with "Probability:" ?
Click to expand...
Probably because counting problems (including combinatorics and Venn diagrams) are often included in chapters on probability; students often tie the ideas together.
blamocur said:
Glad you asked because I assumed that the meaning of @stapel's statement was obvious to native speakers.:)
Click to expand...
I suspect that issues of "or" and "and" are troublesome in every language, because none fully agree with mathematical/logical use, in my experience.

I take the original problem as (intended to be) an exact copy of the problem; it doesn't read like a faulty paraphrase:
Stardust1 said:
In Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
Click to expand...
My first idea to "correct" the wording was to take it as "12 students each study only German, and only Italian", which is a common way to interpret such a statement in English; but that would make the answer trivial.

stapel said:
I suspect that the "and" in "German and Italian" is meant to be an "or". If so, then the exercise solves nicely.
Click to expand...
So, how did you take it, that had a nice solution? I tried several possibilities, and making a literal replacement (which I would take to mean "study German and/or Italian and nothing else") made it particularly difficult.

I'm still probably missing something simple.
 
Using the attached Venn diagram I can see three possible interpretations of the problem so far:
  1. IG = 12
  2. I + G + IG = 12
  3. I + G = 12
Please feel free to provide correct English translations :)
  1. venn2.png
 
I take the problemmatic sentence to mean "11 students study only French, 12 students study only German, 12 student study only Italian, and only 5 students study all 3 languages."

Code: 
Italian             German
   ---------   ---------
 /          / \          \
|   12     |   |   12     |
|          | a |          |
|        --|---|--        |
 \     / b  \5/ c \      /
   ---------   ---------
      |            |
      |     11     |
       \          /
         --------  French

This yields three equations in three unknowns.
 
stapel said:
I take the problemmatic sentence to mean "11 students study only French, 12 students study only German, 12 student study only Italian, and only 5 students study all 3 languages."

Code: 
Italian             German
   ---------   ---------
 /          / \          \
|   12     |   |   12     |
|          | a |          |
|        --|---|--        |
 \     / b  \5/ c \      /
   ---------   ---------
      |            |
      |     11     |
       \          /
         --------  French

This yields three equations in three unknowns.
Click to expand...
That's the interpretation of "and" that I rejected as trivial: It directly tells you the answer, that 12 study only Italian.
 
Sorry guys, there's been a small mistake. Here's the actual question:
At Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian, 15 students study only French and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
P.S Thanks for being so kind.
 
Stardust1 said:
Sorry guys, there's been a small mistake. Here's the actual question:
At Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian, 15 students study only French and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
P.S Thanks for being so kind.
Click to expand...
Now I have to ask you to (a) do as you were asked in #2, and show us what you have tried and where you are stuck, and (b) try using some of the ideas we've shown you.

This problem now is particularly easy; have you tried filling in a Venn diagram, as we showed?
 
Stardust1 said:
Sorry guys, there's been a small mistake. Here's the actual question:
At Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian, 15 students study only French and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
P.S Thanks for being so kind.
Click to expand...
Thank you for the correction. Now please review the "Read Before Posting" message, and reply with a clear listing of your steps so far, starting with your Venn diagram. Thank you!
 
Stardust1 said:
Sorry guys, there's been a small mistake. Here's the actual question:
At Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
11 students study only French, 12 students study only German and Italian, 15 students study only French and Italian and only 5 students study all 3 languages.
How many students study only Italian at Prime High School?
P.S Thanks for being so kind.
Click to expand...
As I read this correction we get: [imath]\#(I\cap G\cap F)=5[/imath]; [imath]\#[(I\cap G)\setminus F]=12[/imath];
[imath]\#[(I\cap F)\setminus G]=15[/imath].
Using the fact that the numbers in each Venn circle add to [imath]40[/imath], can you finish?



[imath][/imath][imath][/imath][imath][/imath]
 
Stardust1 said:
At Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
Click to expand...
What does that "each" mean?

Does it mean:

Italian language class has 40 students​
German language class has 40 students​
French language class has 40 students​

Or

The total number of students (Italian + German + French) in whole grade (sometimes referred to as "class") is 40 ?​
 
khansaheb said:
What does that "each" mean?

Does it mean:

Italian language class has 40 students​
German language class has 40 students​
French language class has 40 students​

Or

The total number of students (Italian + German + French) in whole grade (sometimes referred to as "class") is 40 ?​
Click to expand...
That's how I initially read the problem (though not by thinking that way -- I just didn't read carefully, and am accustomed to problems that tell the total number of students); but the word "class" is implicitly defined:
Stardust1 said:
In Prime High School, there are 3 language classes - Italian, German and French.
There are 40 students in each class.
Click to expand...
 
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